Information on Result #1754224
Digital (170, 185, 1677847)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2185, 1677847, F2, 5, 15) (dual of [(1677847, 5), 8389050, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(223, 127, F2, 5, 7) (dual of [(127, 5), 612, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 23, 127)-net over F2, using
- linear OOA(2162, 1677720, F2, 5, 15) (dual of [(1677720, 5), 8388438, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 5-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- linear OOA(223, 127, F2, 5, 7) (dual of [(127, 5), 612, 8]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (171, 186, 1677847)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (172, 187, 1677847)-net over F2 | [i] | ||